Eric Hamrick was eager to get his hands on newly minted Facebook Inc. stock, placing an order for 500 shares at 6 a.m. Friday before the company's debut on the Nasdaq Stock Market.

The order to buy shares for as much as $49 apiece never made it through. By 11:30 a.m., after the opening of the stock was delayed by a half hour, Mr. Hamrick got nervous and tried to cancel his order. But his online brokerage, Scottrade, displayed the cancellation as "pending," leaving him wondering whether he had bought shares or had...